Question

The investigating team suspected that there were differences in the cost of repairing cars in workshop I and workshop II. The investigating team suspected that the costs raised by workshop I were greater than workshop II. For that they tested the repair of 15 cars in each workshop to see the cost of repairs.The decision of the right hypothesis to prove the suspicion above is a. H0 : μ1- μ2­ = 0; HA : μ1- μ2­ ≠ 0

b. H0 : μ1- μ2 ≥ 0; HA : μ1- μ2 < 0
c. H0 : μD ≥ 0; HA : μD < 0 with μD = μ2- μ1
d. H0 : μD = 0; HA : μD ≠ 0 with μD = μ2- μ1
e. H0 : μ1- μ2 = 0; HA : μ1- μ2 ≥ 0

Answer 1

`H0 : \muD = 0\\\\ H_A : \mu D \\eq0 \text{ with }\ \mu D = \mu2- \mu1`

Explanation:

Let
`\mu_1` and
`\mu_2` are the mean costs raised by workshop I and workshop II respectively.

Given claim :The costs raised by workshop I were greater than workshop II.

i.e.
`\mu_1>\mu_2\ or\ \mu_1-\mu_2>0`

Since it does not contain equals sign therefore we consider it as the alternative hypothesis.

The null hypothesis will be just opposite of this.

i.e.
`H_0:\mu_1-\mu_2\leq0`

Hence, The decision of the right hypothesis to prove the given suspicion:-

`H_0:\mu_1-\mu_2\leq0\\\\H_1:\mu_1-\mu_2>0`

`\text{If }\ D=\mu_1-\mu_2`, then

`H0 : \mu D = 0\\\\ H_A : \mu D \\eq0 \text{ with }\ \mu D = \mu_2- \mu_1`